I. TRUE OR FALSE (6 pts each). No points will be given without a short explanation of your answer. 1. An indifference curve is the set of consumption bundles that a consumer can afford, and between any two of which the consumer is indifferent. 2. If income increases by 20%, the price of good 1 decreases by 10%, and the price of good 2 does not change, then the consumer must be better off. 3. If the price of good 2 is $p2 and the consumer's income is $m, then the consumer's income measured in units of good 2 in m 2 4. The binary relation "harder or equally hard" used to compare Econ 201 assignments is complete and transitive. 5. The demand function specifies the quantity consumed for any price p > 0 when the consumer's income is fixed at some level m. II. PROBLEMS 1. Budget lines and sets (30 pts) Always briefly explain your answers! A consumer consumes two goods: wraps and tea, with respective quantities x and x2. Suppose the price of a wrap is $5 and the price of a cup of tea is $1. The consumer's weekly income is m = $70. (a) Write the budget constraint inequality and plot the budget line. Put tea on the horizontal axis and label your graph (intercepts, axes, etc.) clearly. (b) Suppose the consumer can go to two different restaurants which sell wraps and tea, M or N. At restaurant M, for every 5 wraps consumed in a week, the customer receives one free wrap. At restaurant N, for the first five teas consumed in a week, a customer receives two free teas (after that any additional tea is sold at the regular price). Plot the consumer's budget line if she goes to restaurant M. On the same graph, plot in different color her budget line if she went to N instead. (c) Plot an example indifference curve of a consumer who would optimally choose to go to restaurant M. Do the same for restaurant N (plot a different example indifference curve). (d) Suppose that now both promotions in (b) and (c) are over but the consumer decided to never consume more than 1 wrap per day (i.e., a maximum total of 7 wraps for the week). Draw the consumer's budget line with this condition imposed. 2. Optimal choice and demand (40 pts) Always briefly explain your answers! Yi has preferences over two goods, drinks with quantity d and dollars spent on food, f and has the utility function f2 u(f, d) = 3d+3 20 = $1 per unit. The price per drink is $3 and Yi's income is m dollars. Call dollars spent on food good 1. (a) Explain that the price of good 1 (dollars spent on food) is p1 (b) Are the two goods perfect substitutes for Yi? Why or why not? (c) Suppose m = $50. Can Yi afford the bundle (10,10)? If he can afford it, is there another affordable bundle (give a specific example) that he strictly prefers to (10, 10)? [Hint: use monotonicity of preferences]. (d) Write down Yi's consumer's problem of maximizing his utility subject to his budget constraint and find his demand function for each of the two goods for any income level m 0. Plot Yi's Engel curve for good 1. (e) What is Yi's optimal consumption bundle if m = $50? If his income was $15 instead, what would be his optimal bundle? (f) Let m = $50 and suppose the price of drinks rose to $4. If the government gave Yi a $14 lump-sum income subsidy in addition to his $50, what would be Yi's budget set (plot it on a graph)? What is his new optimal bundle? Is he better off or worse off than in part (e) when he had m= $50 but drinks were cheaper?